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Find the no. of seven digit integers with sum of digits = 11 and formed by using the digits 1,2 and 3 only ?
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7 digit number by 1,2,3 and sum 11

The number will be combination of 2 2 2 2 1 1 1 =$\frac{7!}{4!3!}$=35

or, 3 3 1 1 1 1 1=$\frac{7!}{2!5!}$=21

or, 3 2 2 1 1 1 1=$\frac{7!}{2!4!}$=105

So, total such numbers possible=35+21+105=161
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